An exhaust purification system for an internal combustion engine is known in the art, in which an exhaust purification catalyst is arranged in an engine exhaust passage and a hydrocarbon feed valve is arranged upstream of the exhaust purification catalyst in the engine exhaust passage, wherein a precious metal catalyst is carried on an exhaust gas flow surface of the exhaust purification catalyst and basic exhaust gas flow surface parts are formed around the precious metal catalyst, wherein the exhaust purification catalyst has the property of reducing the NOX contained in exhaust gas if a concentration of hydrocarbons flowing into the exhaust purification catalyst is made to vibrate at within a predetermined range of amplitude and with a period within a predetermined range of period and has the property of a storage amount of NOX contained in exhaust gas increasing if a vibration period of the hydrocarbon concentration is made longer than the predetermined range of period, and wherein a first NOX purification method configured to inject hydrocarbons from the hydrocarbon feed valve with a period within the predetermined range of period to thereby purify the NOX contained in the exhaust gas and a second NOX purification method configured to make an air-fuel ratio of exhaust gas flowing into the exhaust purification catalyst rich with a period longer than the predetermined range of period to thereby make the exhaust purification catalyst release the stored NOX to purify the NOX are selectively used (for example, see PTL 1). In this exhaust purification system, when a temperature of the exhaust purification catalyst is lower than a limit temperature, the second NOX purification method is used, while when the temperature of the exhaust purification catalyst is higher than the limit temperature, the first NOX purification method is used. Further, in the second NOX purification method, rich control configured to inject additional fuel in addition to fuel for combustion in a combustion chamber to make the air-fuel ratio of the exhaust gas flowing into the exhaust purification catalyst rich, is performed in order to purify NOX.